The direct answer to your question is pretty straightforward and reassuring, I think. That being: There is no apparent evidence that any actual, in-the-wild attacks have occurred where malware has written to the firmware of a sound card. (Meaning I don't recall ever having read of a confirmed case of that happening, and some searching on Google revealed no such confirmed cases either.) In fact, I haven't even read of or discovered any proof of concept cases where that has been demonstrated. (Note: If anybody knows of any source that documenting otherwise please feel invited to share it in the comments.)
And really, I don't know that that lack of documented cases is terribly surprising. Discrete sound cards really aren't that common in today's PCs, and if you wanted to write malware that could hide in a sound card's firmware you'd probably have to have to develop and test different code for each make and model of each card you wanted to be able to infect. A bit like the NSA had to do with its hard drive firmware-infecting efforts. So, perhaps it makes some intuitive sense that we haven't yet seen malware that tries to persist in sound card firmware.
So, from a practical standpoint I don't think badusb-like firmware infection is really something that's worth devoting any real worry to. There's no indication that any malware trying to use that approach is running around out there in the wild (at this point, anyway), let alone anything prevalent enough to necessitate taking the course of junking a partly-customized sound card out of fear of it.
That being said... I'll close with two caveats:
Rewriting the firmware of internal PC components is indisputably possible, and has (although rarely) actually occurred in the wild. Aside from stuff that hits main BIOS or UEFI, security researchers have indeed done proof of concept demonstrations of firmware-alteration in network cards. There is some indication that USB host controllers are quite viable targets, and possible attacks on internal components in general have often been written about as feasible. And, as mentioned above there is open source confirmation that highly-targeted, real-world attacks involving hard drive firmware alteration have occurred. So it's not really that sound card firmware-alteration would be an out-of-the-blue, amazing new technical surprise.
- If you're a target worth detailed attention from the NSA or other very-high-end nation-state threats then pretty much any theoretically plausible attack has to be considered as something you need to be on guard against. And getting the firmware on a sound card altered by sophisticated, persistent malware would definitely be in the category. On the other hand, it you were a target of such importance the question of whether or not to junk a sound card would probably be pretty far down on your very, very, very long list of security matters to worry about.
So, you would almost certainly be just fine.
edit: Replying to question's edit #3:
Yeah, I think we are talking about the same thing, although in slightly different ways and terms. If I understand you you're asking about whether a good, correctly-operating sound card can get a malware infection of some kind and afterward turn into a maliciously operating perhipheral that tries to lie to your computer that it's a USB keyboard (or another Human Interface Device) and start feeding it "key presses" that, say, open a command prompt and enter commands into the system, right?
Well, the way that that malicious attack happens with something like a USB drive is that the firmware on the drive that tells the drive what it's supposed to do has to get overwritten with new instructions. That's why a USB drive can start to act like a keyboard or other human interface peripheral: because the overwritten, maliciously-changed firmware tells it to. (More details about exactly how that works to make badUSB possible are here.) Unless you can correctly rewrite the firmware for a USB drive to do what you want to do, create an attack that alters the firmware of USB drives you want to turn malicious, and finally expose a USB drive to that attack something like badUSB can't happen.
Basically the same thing is like case with stuff like BIOS chips in PCs, or with network cards, or hard drives, or graphics cards, or, yes, sound cards. And that's where you get to what my answer discusses: while it might be theoretically possible that an attacker could pull off what you suggest, there's no evidence right now that any such attacks have occurred in real life with sound cards.
edit: replying to question edit #4
Okay, so I think I'll give an answer one more quick shot here. I have reread the question and the subsequent edits with care. Although I'm still not exactly quite sure why we're not on the same page, perhaps one more quick effort can fix that. So...
First, If the question you're asking is: "Assume this USB sound card has somehow been infected by BADUSB or something very like that.. could it do these BadUSB attack things?" I suppose the only responsible answer I could give with be: if something can be infected by BadUSB, one really should err on the safe side and assume that it could act like BadUSB. Meaning it could potentially spread nastiness to a PC or device that you might plug it into.
Still assuming the card is infected with BADUSB, if you wanted to use it anyway you might ask "Are there things that I might do that might lessen or almost eliminate the risk that my PCs and other devices might get infected with badUSB themselves from the sound card?" Well, I think the answers to this question and this question address that more comprehensively than I could. So I'll just point to those, aside from offering the generic observation that introducing any element that you know to be infected with malware to your technical setup invariably brings at least some degree of risk with doing so. Even if good countermeasures & mitigations are available to reduce that risk, that's a different thing from eliminating that added risk altogether.
But all of what I just said is based on starting with that one absolutely critical assumption: that your recently acquired USB sound device is infected with BadUSB or something like it. And to reiterate what I said previously: As you've laid out the facts there is a very, very, very low likelihood that that is actually true in your case. There is no recorded incidence (That I've found, anyway. Or that anyone else has mentioned.) of an infected USB sound card occurring anywhere, either in the wild or even in a researcher's lab. At all. Thus, my original non-advice advice: unless you would be a target of exceptional importance to some person or organization with major, major technical chops worrying about the firmware in your purchased USB sound card being infected with anything almost certainly isn't worth expending the mental energy to do so.
